Simplify fifth root of 8x^3y* fifth root of 4x^4y

$\sqrt[5]{8 x^{3} y} \cdot \sqrt[5]{4 x^{4} y}$

Multiply $\sqrt[5]{8 x^{3} y} \sqrt[5]{4 x^{4} y}$ .

Combine using the product rule for radicals.

$\sqrt[5]{8 x^{3} y (4 x^{4} y)}$

Multiply $4$ by $8$ .

$\sqrt[5]{32 x^{3} y (x^{4} y)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[5]{32 x^{4 + 3} y \cdot y}$

Add $4$ and $3$ .

$\sqrt[5]{32 x^{7} y \cdot y}$

Raise $y$ to the power of $1$ .

$\sqrt[5]{32 x^{7} (y^{1} y)}$

Raise $y$ to the power of $1$ .

$\sqrt[5]{32 x^{7} (y^{1} y^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[5]{32 x^{7} y^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt[5]{32 x^{7} y^{2}}$

Rewrite $32 x^{7} y^{2}$ as ${(2 x)}^{5} (x^{2} y^{2})$ .

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} x^{7} y^{2}}$

Factor out $x^{5}$ .

$\sqrt[5]{2^{5} (x^{5} x^{2}) y^{2}}$

Rewrite $2^{5} x^{5}$ as ${(2 x)}^{5}$ .

$\sqrt[5]{{(2 x)}^{5} x^{2} y^{2}}$

Add parentheses.

$\sqrt[5]{{(2 x)}^{5} (x^{2} y^{2})}$

Pull terms out from under the radical.

$2 x \sqrt[5]{x^{2} y^{2}}$